Source code for preliz.distributions.halfcauchy
import numpy as np
from pytensor_distributions import halfcauchy as ptd_halfcauchy
from preliz.distributions.distributions import Continuous
from preliz.internal.distribution_helper import eps, pytensor_jit, pytensor_rng_jit
from preliz.internal.optimization import optimize_ml
[docs]
class HalfCauchy(Continuous):
r"""
HalfCauchy Distribution.
The pdf of this distribution is
.. math::
f(x \mid \beta) =
\frac{2}{\pi \beta [1 + (\frac{x}{\beta})^2]}
.. plot::
:context: close-figs
from preliz import HalfCauchy, style
style.use('preliz-doc')
for beta in [.5, 1., 2.]:
HalfCauchy(beta).plot_pdf(support=(0,5))
======== ==========================================
Support :math:`x \in [0, \infty)`
Mean undefined
Variance undefined
======== ==========================================
Parameters
----------
beta : float
Scale parameter :math:`\beta` (``beta`` > 0)
"""
def __init__(self, beta=None):
super().__init__()
self.support = (0, np.inf)
self._parametrization(beta)
def _parametrization(self, beta=None):
self.beta = beta
self.params = (self.beta,)
self.param_names = ("beta",)
self.params_support = ((eps, np.inf),)
if self.beta is not None:
self._update(self.beta)
def _update(self, beta):
self.beta = np.float64(beta)
self.params = (self.beta,)
self.is_frozen = True
[docs]
def pdf(self, x):
return ptd_pdf(x, self.beta)
[docs]
def cdf(self, x):
return ptd_cdf(x, self.beta)
[docs]
def ppf(self, q):
return ptd_ppf(q, self.beta)
[docs]
def logpdf(self, x):
return ptd_logpdf(x, self.beta)
[docs]
def entropy(self):
return ptd_entropy(self.beta)
[docs]
def mean(self):
return ptd_mean(self.beta)
[docs]
def mode(self):
return ptd_mode(self.beta)
[docs]
def var(self):
return ptd_var(self.beta)
[docs]
def std(self):
return ptd_std(self.beta)
[docs]
def skewness(self):
return ptd_skewness(self.beta)
[docs]
def kurtosis(self):
return ptd_kurtosis(self.beta)
[docs]
def lmoment1(self):
return ptd_lmoment1(self.beta)
[docs]
def lmoment2(self):
return ptd_lmoment2(self.beta)
[docs]
def lmoment3(self):
return ptd_lmoment3(self.beta)
[docs]
def lmoment4(self):
return ptd_lmoment4(self.beta)
[docs]
def rvs(self, size=None, random_state=None):
random_state = np.random.default_rng(random_state)
return ptd_rvs(self.beta, size=size, rng=random_state)
def _fit_moments(self, mean, sigma):
self._update(sigma)
def _fit_mle(self, sample):
optimize_ml(self, sample)
@pytensor_jit
def ptd_pdf(x, beta):
return ptd_halfcauchy.pdf(x, beta)
@pytensor_jit
def ptd_cdf(x, beta):
return ptd_halfcauchy.cdf(x, beta)
@pytensor_jit
def ptd_ppf(q, beta):
return ptd_halfcauchy.ppf(q, beta)
@pytensor_jit
def ptd_logpdf(x, beta):
return ptd_halfcauchy.logpdf(x, beta)
@pytensor_jit
def ptd_entropy(beta):
return ptd_halfcauchy.entropy(beta)
@pytensor_jit
def ptd_mean(beta):
return ptd_halfcauchy.mean(beta)
@pytensor_jit
def ptd_mode(beta):
return ptd_halfcauchy.mode(beta)
@pytensor_jit
def ptd_median(beta):
return ptd_halfcauchy.median(beta)
@pytensor_jit
def ptd_var(beta):
return ptd_halfcauchy.var(beta)
@pytensor_jit
def ptd_std(beta):
return ptd_halfcauchy.std(beta)
@pytensor_jit
def ptd_skewness(beta):
return ptd_halfcauchy.skewness(beta)
@pytensor_jit
def ptd_kurtosis(beta):
return ptd_halfcauchy.kurtosis(beta)
@pytensor_jit
def ptd_lmoment1(beta):
return ptd_halfcauchy.lmoment1(beta)
@pytensor_jit
def ptd_lmoment2(beta):
return ptd_halfcauchy.lmoment2(beta)
@pytensor_jit
def ptd_lmoment3(beta):
return ptd_halfcauchy.lmoment3(beta)
@pytensor_jit
def ptd_lmoment4(beta):
return ptd_halfcauchy.lmoment4(beta)
@pytensor_rng_jit
def ptd_rvs(beta, size, rng):
return ptd_halfcauchy.rvs(beta, size=size, random_state=rng)
